GPS World, November 2009

TIMING FREQUENCY Receiver Design p FIGURE4 Difference between actual and predicted variance at output of discriminator of the local oscillator phase deviation requires only three steps assuming that certain criteria can be met The first requirement is that the averaging times in question must be short relative to the duration at which processes other than white phase and flicker phase modulation begin to dominate the noise characteristics of the oscillator Typically the crossover point between the dominance of these processes and others is above 1 s in averaging interval length when quartz oscillators are concerned Since this article discusses a specific implementation interval of 10 ms within systems expected to be using quartz oscillators it is reasonable to assume that this constraint will be met The second requirement is that the Allan deviation of the given system oscillator must be known for at least one averaging interval within the region of interest Since the Allan deviation follows a linear slope of 1 with respect to averaging interval on a log log scale within the white phase noise region this single value will allow an accurate prediction of the Allan deviation at any other point on the interval and in turn of the phase uncertainty at the 10 ms averaging interval level Letting represent the Allan deviation at a specific averaging interval recall that this quantity is the midpoint average of the standard deviation of fractional frequency error over the averaging interval Scaling this quantity by a frequency of interest results in the standard deviation of the absolute frequency error on the averaging interval By integrating this average difference in frequency deviations over the coherent period of interest one obtains a measure of the standard deviation in degrees of a signal generated by this reference Note that the averaging interval must be identical to the coherent integration time Turning to a practical example if the oscillator in question has a 1 s Allan Deviation of 1 part per hundred billion 1 in 1011 a stability value between that of an OCXO and microcomputer compensated crystal oscillator MCXO standard and shown to be somewhat pessimistic this would scale linearly to be 1e 9 at a 10 ms averaging interval under the previous assumption that the oscillator uncertainty is dominated by the white phasenoise term at these intervals Also for illustration purposes if one assumes the carrier of interest to be the nominal GPS L1 carrier the uncertainty in the local carrier replica due to the local oscillator over a 10 ms coherent integration time becomes When stated in a more readily digested format this represents roughly 15 centimeter second in the line of sight velocity uncertainty In an operating receiver two additional factors modify this effect The first is the previously discussed scaling effect that will tend to exaggerate this effect by a typical factor of 175 as previously discussed The second factor is that this noise contribution is filtered by the bandwidth limiting effects of the local loop filter producing a modification to the noise affecting velocity estimates as well as reduced information about the behaviour of the local oscillator Impact of Apparent Dynamics When considering the error sources within the system it is important to realize which individual sources of error will contribute to estimation errors and which will not One area of potential concern would appear to be the errors in the satellite ephemerides encompassing both the satellite orbit trajectory misrepresentation and the satellite clock error While the errors in the satellite ephemerides are of concern for point positioning they are not of consequence to this application as the apparent error introduced by a deviation of the true orbit from that expressed in the broadcast orbital parameters does not affect the tracking of that satellite at the loop level Additionally while the satellite clock will add uncertainty to the epoch to epoch phase change within each channel independently the magnitude of this change is minimal relative to the contribution of uncertainty due to the variance at the output of the discriminator guaranteed by the low carrier to noise density ratio of a received GNSS signal Since this contribution is uncorrelated between satellites and relatively small compared to other noise contributions affecting these measurements even when compared to the soon to be discontinued Uragan GLONASS satellites that had generally less stable onboard clocks it is likely safe to ignore When compared to the more stable oscillators aboard GPS or GLONASS M satellites it is a reasonable assumption that this will be a dismissible contribution to received signal phase uncertainty change While atmospheric effects present an obstacle which will directly affect the epoch to epoch output of the discriminators it is believed that under conditions that do not include the effects GPS World November 2009 www gpsworld com 34

View the Covers and the Table of Contents pages from every issue of this publication, all gathered together for easy browsing. Just flip pages and zoom as you normally do to see each issue's Cover and Table of Contents, then follow links directly to interesting content.